Was wondering on what would be the real number (scalar) $\gamma$ that needs to be multiplied with each entry in a real rectangular matrix $X_{m\times n}$ such that the Frobenius norm of $X$ equals a given positive value $\alpha$?

i.e, Find a $\gamma$ such that $||\gamma X||_{F}^{2}=\alpha$.

Am expecting that $\gamma$ would be a function of $mn$ and $\alpha$.

Let me know, if there is some condition or notation that I might have left out.

Was posting a question based on an inequality based on the Frobenius norm, but it required this question to be answered to get my notation right in the other question. Thanks